CBSE Class 11 Mathematics Sequences And Series Worksheet Set 01

Multiple Choice Questions

Question. The number of terms in the AP 20, 25, 30, …… 100 are
(a) 16
(b) 17
(c) 18
(d) 19
Answer : B

Question. The sum of three consecutive terms of an AP is 15, and their product is 105, then the common difference is
(a) ±1
(b) ±2
(c) ±3
(d) ±4
Answer : B

Question. If in an AP, first term is 2 and the sum of first five terms is one-fourth of the next five terms, then the 20th terms is
(a) −140
(b) −100
(c) −112
(d) −138
Answer : C

Question. If n terms of GP 3, 3² , 3³ , ..... are needed to give the sum 120, then the value of n is
(a) 2
(b) 3
(c) 4
(d) 5
Answer : C

Question. The rth term of an AP sum of whose first n terms is 2n + 3n² is given by
(a) 6r + 1
(b) 6r −1
(c) 6r
(d) 3r −1
Answer : B

Question. In an AP, if mth term is n and the nth term is m, where m ≠ n, then pth term is
(a) m+n −p
(b) m−n + p
(c) n −m+ p
(d) m+n + p
Answer : A

Question. If the 8th term of a GP is 192 with the common ratio 2, then the 12th term is
(a) 1640
(b) 2084
(c) 3072
(d) 3126
Answer : C

Question. If the third term of GP is 4, then the product of its first 5 terms is
(a) 4³
(b) 4⁴
(c) 4⁵
(d) None of these
Answer : C

Question. The 5th term from the end of the sequence 16, 8, 4, 2, ……1/16 is
(a) 1
(b) 2
(c) 3
(d) 4
Answer : A

Question. 6 arithmetic means between 3 and 24 are
(a) 6, 9, 12, 15, 18 and 21
(b) 6, 9, 10, 15, 18 and 21
(c) 6, 8, 10, 15, 18 and 21
(d) 6, 9, 12, 13, 18 and 21
Answer : A

Question. The sum of an infinite GP is 80/9 and its common ratio is −4/5 then its first term is equal to
(a) 10
(b) 14
(c) 15
(d) 16
Answer : D

Asserion-Reasoning MCQs

Directions Each of these questions contains two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of the which is the correct answer. You have to select one of the codes (a), (b), (c) and
(d) given below.
(a) A is true, R is true; R is a correct explanation of A.
(b) A is true, R is true; R is not a correct explanation of A.
(c) A is true; R is false
(d) A is false; R is true.

Question. Assertion (A) The sum of first 20 terms of an AP, 4, 8, 12, … is equal to 840.
Reason (R) Sum of first n terms of an AP is given by S_n = n/2 [2a + (n -  1)d], where a = first term and d = common difference
Answer : A

Question. Assertion (A) The sum of the series 3/√5 + 4/√5 + √5 + …… 25 terms is 75√5.
Reason (R) If 27, x, 3 are in GP, then x = ± 4.
Answer : C

Question. Assertion (A) If nth term of a sequence is a_n = n²/2ⁿ, then its 7th term is 49/128
Reason (R) If nth term of a sequence is a_n = n(n - 2) / n + 3, then its 20th term is 323/22
Answer : C

Question. Assertion (A) The fourth term of a GP is the square of its second term and the first term is −3, then its 7th term is equal to 2187.
Reason (R) Sum of first 10 terms of the AP 6, 8, 10, ……… is equal to 150.
Answer : D

Question. Assertion (A) If 5th and 8th term of a GP be 48 and 384 respectively, then the common ratio of GP is 2.
Reason (R) If 18, x, 14 are in AP, then x = 16.
Answer : B

Question. Assertion (A) If the nth term of a sequence is a_n = 4n − 3. Here, a₁₇ and a₂₄ are 65 and 93 respectively.
Reason (R) If the nth term of a sequence is an d_n = (−1)^{n − 1} n³ . Here, 9th term is 729.
Answer : B

Question. Assertion (A) The sum of first n terms of the series 5 + 55 + 555 + … is 5/9 [10(10n - 1) / 9 - n ]
Reason (R) General term of an AP is T_n = a + (n − 1)d , where a = first term and d = common difference.
Answer : B

Case Based MCQs

A sequence whose terms increases or decreases by a fixed number, is called an Arithmetic Progression (AP). In other words, we can say that, a sequence is called an arithmetic progression if the difference of a term and the previous term is always same i.e. a_n+1 − a_n = constant for all n. This constant or same difference is called the common difference of an AP and it is denoted by d. In an AP, we usually denote the first term by a, common difference by d and the nth term by a_n or T_n defined as T_n = a_n = a + (n - 1)d Also, l = a + (n −1)d, where l is the last term of the sequence. The sum of n terms, S_n of this AP is given by S_n = n/2 [2a + (n - 1)d] Also, if l be the last term, then the sum of n terms of this AP is S_n = n/2 (a + l)

Based on the above information, answer the following questions.

Question. If nth term of an AP is given by a_n = 2n² +1, then its 10th term is equal to
(a) 200
(b) 301
(c) 400
(d) Given sequence is not an AP
Answer : D

Question. 11th term of an AP 11, 18, 25, … is equal to
(a) 80
(b) 81
(c) 71
(d) 70
Answer : B

Question. If the sum of n terms of an AP is given by S_n = 3n + 2n² , then the common difference of the AP is
(a) 3
(b) 2
(c) 6
(d) 4
Answer : D

Question. If 9 times the 9th term of an AP is equal to 13 times the 13th term, then the 22nd term of the AP is
(a) 0
(b) 22
(c) 198
(d) 220
Answer : A

Question. Let S_n denote the sum of the first n terms of an AP, if S_2n = 3S_n , then S_3n : S_n is equal to
(a) 4
(b) 6
(c) 8
(d) 10
Answer : B

A student of class XI draw a square of side 10 cm. Another student join the mid-point of this square to form new square. Again, the mid-points of the sides of this new square are joined to form another square by another student. This process is continued indefinitely.

Based on above information, answer the following questions.

Question. The side of fourth square is (in cm)
(a) 5
(b) √5/2
(c) √5
(d) None of these
Answer : D

Question. The area of the fifth square is (in sq cm)
(a) 25/2
(b) 50
(c) 25
(d) 25/4
Answer : D

Question. The perimeter of the 7th square is (in cm)
(a) 10
(b) 20
(c) 5
(d) 5/2
Answer : C

Question. The sum of areas of all the square formed is (in sq cm)
(a) 150
(b) 200
(c) 250
(d) None of these
Answer : B

Question. The sum of the perimeter of all the square formed is (in cm)
(a) 80 + 40√2
(b) 40 + 40√2
(c) 40
(d) None of these
Answer : A

 Please click on below link to download CBSE Class 11 Mathematics Sequences And Series Worksheet Set A